# Quasinormal modes of three-dimensional rotating Ho\v{r}ava AdS black hole and the approach to thermal equilibrium

## TL;DR

This paper calculates the quasinormal modes of a scalar field in a rotating three-dimensional Hořava AdS black hole, revealing stability and insights into the system's thermalization process under Lorentz invariance breaking.

## Contribution

It provides the first analysis of quasinormal modes in a rotating Hořava AdS black hole, exploring the effects of Lorentz invariance violation on stability and thermalization.

## Key findings

- Scalar field propagation is stable in this background.
- Different solutions reach thermal equilibrium at different times.
- Lorentz invariance breaking influences QNM characteristics.

## Abstract

We compute the quasinormal modes (QNMs) of a massive scalar field in the background of a rotating three-dimensional Ho\v{r}ava AdS black hole, and we analyze the effect of the breaking of the Lorentz invariance on the QNMs. Imposing on the horizon that there are only ingoing waves and at infinity the Dirichlet boundary conditions and the Neumann boundary condition, we calculate the oscillatory and the decay modes of the QNMs. We find that the propagation of the scalar field is stable in this background and employing the holographic principle we find the different times of the perturbed system to reach thermal equilibrium for the various branches of solutions.